Hi! This is my personal experience this application cycle: I did not have any firm offers until very recently, when I got off the waitlist at two different programs. I stayed in constant contact with the DGAs at these two programs (particularly with the director at the program that was my first choice), and I believe that it played a big role in eventually receiving an offer.
Seeing as it is very close to the April 15th deadline, you really have nothing to lose (and potentially a lot to gain!) by e-mailing the graduate admissions director at Georgetown. Waitlists are fluid and I think that expressing your strong interest in the program can only put you in a better position. Good luck, I hope you receive an offer soon!